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Question
Find the values of x and y, if \[2\begin{bmatrix}1 & 3 \\ 0 & x\end{bmatrix} + \begin{bmatrix}y & 0 \\ 1 & 2\end{bmatrix} = \begin{bmatrix}5 & 6 \\ 1 & 8\end{bmatrix}\]
Solution
\[Given: 2\begin{bmatrix}1 & 3 \\ 0 & x\end{bmatrix} + \begin{bmatrix}y & 0 \\ 1 & 2\end{bmatrix} = \begin{bmatrix}5 & 6 \\ 1 & 8\end{bmatrix}\]
\[ \Rightarrow \begin{bmatrix}2 & 6 \\ 0 & 2x\end{bmatrix} + \begin{bmatrix}y & 0 \\ 1 & 2\end{bmatrix} = \begin{bmatrix}5 & 6 \\ 1 & 8\end{bmatrix}\]
\[ \Rightarrow \begin{bmatrix}2 + y & 6 + 0 \\ 0 + 1 & 2x + 2\end{bmatrix} = \begin{bmatrix}5 & 6 \\ 1 & 8\end{bmatrix}\]
\[ \Rightarrow \begin{bmatrix}2 + y & 6 \\ 1 & 2x + 2\end{bmatrix} = \begin{bmatrix}5 & 6 \\ 1 & 8\end{bmatrix}\]
\[ \therefore 2 + y = \text{5 and }2x + 2 = 8\]
\[ \Rightarrow y =\text{ 5 - 2 and } 2x = 8 - 2\]
\[ \Rightarrow y = \text{3 and }2x = 6\]
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